Question

Variation of a force in a certain region
is given by F = 6x2 - 4x - 8. It displaces
an object from x = 1 m to x = 2 m in this
region. Calculate the amount of work
done. [Ans: Zero]​

Answer 1

Answer:

Integreting F gives2x^3 - 2x^2 - 8x

acc to the ques x is from 2 to 1 now keeping values we get

14 - 6 - 8= 0

Answer 2

Answer:

The amount of work  done is zero.

Explanation:

Given that,

Force $F= 6x^2-4x-8$

It displaces  an object from x = 1 m to x = 2 m in this  region.

We need to calculate the work done

Using formula of work done

$dW=F\cdot dx$

Put the value into the formula

$dW=( 6x^2-4x-8)dx$

Integrating on both side within the limit

$\int_{0}^{w}{dW}=\int_{1}^{2}{6x^2}dx-\int_{1}^{2}{4x}dx-\int_{1}^{2}{8}dx$

$W=6(\dfrac{x^3}{3})_{1}^{2}-4(\dfrac{x^2}{2})_{1}^{2}-8(x)_{1}^{2}$

$W=6(\dfrac{2^3}{3}-\dfrac{1^3}{3})-4(\dfrac{2^2}{2}-\dfrac{1^2}{2})-8(2-1)$

$W=0$

Hence, The amount of work  done is zero.